Fed up means angry. When something has been bothering you for a while and finally you just can't take it, you're fed up. Bored is when you lack interest in something. For example, I was so bored at work today. Or, I am fed up that my sister keeps borrowing my clothes.

I'm 'fed up' with the weather, it's been raining for a week. I'm 'bored' with my music, I need to get some new cd's.

Good answer, kw102290. I'm fed up of being bored :) or maybe I'm just bored of being fed up :)